Week 4 - Differentiated instruction

This week we talked about how to incorporate differentiated instruction in the math class. Before this year I wasn't sure how to fit differentiated instruction in the math class. Would I have to make separate lesson plans for the different learning styles or have dedicated time in each lesson plan towards each of the learning styles? I didn't realize how simple it could be to incorporate it into a lesson, such as the activity below.

With this activity we matched the different visual representations of each pattern. This represents differentiated instruction because there are many different methods to get to this final stage. Some of the students in class started matching graphs to the table of values because those were the two that they understood better. Others started with the equation and the graph because those made more sense to them. With each of these 4 representations, all students would be able to complete this exercise using their own strengths in mathematics. A lot of work went into creating this activity, but the work is definitely worth it because it helps each student to be able to perform this task.

The Knowing and responding to learners in Mathematics (2015) article talks about why differentiated instruction is important in a math class. High school students are growing at different speeds. Some may be farther ahead in their math understanding than others, so some students will be better at spatially understanding the mathematics whereas other students will be better at taking a visual representation of a math concept and connecting it to the abstract mathematics. By incorporating all of the different learning styles, we would be able to help each student to understand the math concepts in the lesson better. In order to successfully incorporate differentiated instruction we need to "balanc[e] understanding of mathematical concepts with procedural fluency" (1). Using the example above, we couldn't just get the students that prefer working with graphs to work only with graphs, they would still have to work with the pattern, table, and rule. However, by letting them choose which one to work with first, they are able to pick the one they understand best to help them work with the other representations that they don't understand as well, increasing their knowledge of the entire concept of linear equations.

I would like to do something similar to this in my future math class because I feel that it would help all the students to get a better feel and understanding of the concept.

Week 3 - Math Manipulatives

In class this week we worked with multiple manipulatives that can be used to explore different concepts in mathematics. When I was in high school we did not use math manipulatives often, even though it is in the curriculum. In my opinion that is because it is often assumed that the students in academic courses are more capable of understanding the concepts without the need of seeing it visually represented in front of them. I believe that manipulatives should be incorporated in every math course, for all levels of learning. This way the concepts are able to make sense in a concrete sense, as well as in an abstract sense.

When I have a math class I will try to use manipulatives whenever it would work in the lessons because they help us to have a better understanding of the math behind what is being learned. In class this week I was able to understand better the math behind the equation n*(n+1)/2 as the equation for the sum of 1 + 2 + 3 + … + n. Before this class I knew that the equation and the sum meant the same thing, but I did not fully understand why until I used the snap cubes to find out that by doubling the amount of blocks I had made a rectangle with dimensions n x (n+1), which is how we arrived at the previous equation. The snap cubes helped me to see the abstract equation in a concrete way so that 

I was able to better understand why the equation is equal to the sum.

Manipulatives can help any math student to have a better understanding of what they are learning and that is why I believe they should be used as often as possible.

Week 2 - Problem Solving

In class this week we were asked: 'would you rather have $500 or quarters stacked up as tall as you?' and later we were also given a tug of war problem shown below.

We were asked these questions and then left on our own to find a way to come up with a solution. With this method of teaching we were all able to explore our own way of problem solving. After each coming to a solution we then got into groups and discussed how we each came to our solutions. We found that there were many different ways to solve each of these questions all coming to the same answer. This shows that there is no one way to solve a math problem and that students should be encouraged to express their own ideas on how to solve the given problem

In the Dan Meyer video on the math classroom, he talked about taking the steps out of math problems and letting the students come up with the necessary steps to reach the solution. This method of teaching brings problem solving into the classroom and it also helps the students to get a better understanding of math. Instead of giving the students a system or formula to solve the problem, they have to figure out what information they will need to find the answer and what steps they would have to go through to get there. This promotes critical thinking and it helps the students to determine what knowledge is important and what is not necessary for solving the question. I would like to incorporate this method to student problem solving in my future math classes.

Week 1

Hello, my name is Colleen and I'm a teacher candidate at Brock University. I am in the concurrent education program year 5 and my teachables are math and French for grades 7-12. I have recently gotten married and I am excited to start this year off right. This blog is for the math education course EDBE 8F83 and I will be using it to keep track of what is going on throughout the coursework and to reflect on what we have been taught and how it could be incorporated into the classroom setting. I will be blogging weekly to see how everything will progress and hopefully it will help to prepare me for my placements later on in the year.

Throughout this course I hope to learn how to get my students motivated about learning mathematics. I have seen a stigma around mathematics that has made students disinterested in mathematics to the point of hating even the word "math". I would like to show the students that math can be fun as well as how math relates to the real world, while still teaching the students the curriculum that they are supposed to learn. I would also like to see the connections between this course and my previous math courses as well as my previous education courses to see how math and education can be combined to form the math classroom. I am looking forward to this upcoming year and all that it has to offer to prepare myself and the other teacher candidates for the following years to come.